Liability insurance covers you when damage or injuries are done to others. Property damage liability covers you if your car damages someone else's property, not your own vehicle's damages. For your vehicle to be covered for damages you would need to have physical damage coverages.

Physical damage coverages include collision and comprehensive. In the case of your vehicle catching on fire for an unexplained reason, you would need comprehensive insurance on your vehicle.

Comprehensive covers your vehicle for losses other than collision. This can include covering for your car if it is stolen, damaged by flood, fire or animals among other things. Without this coverage and with only liability on your vehicle, unfortunately a fire of unknown origin would not be covered.